UQSay #97

The ninety-seventh UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, March 26, 2026.

2–3 PM — Anthony Quintin (CEA DIF)

Optimal experimental designs based on the cross-entropy method for planning fracture toughness tests

Nuclear reactor pressure vessels undergo progressive embrittlement under neutron irradiation, monitored through the Master Curve theory which estimates a reference temperature T0. The core challenge is obtaining a reliable estimate of T0 from a very limited number of specimens. The work pursues two objectives. First, developing a numerical twin of fracture toughness test campaigns based on finite element simulations coupled with a Beremin model calibrated via Bayesian inference. Second, building a decision-making tool to optimize experimental planning within the framework of Bayesian Optimal Experimental Design, which seeks to determine the experimental conditions maximizing the information gained from a limited number of observations.

To this end, the approach relies on a Bayesian optimization method aimed at identifying test temperature sequences that minimize uncertainty on T0. The problem is formulated as a constrained combinatorial optimization, where the criterion to maximize is an expected information gain (entropy). Temperature sequences are modeled as homogeneous first-order discrete-time Markov chains, whose transition matrix is optimized via the Cross-Entropy Method. The resulting method yields a transition matrix that serves as a directly interpretable sequential decision rule. The proposed methodology is inherently general and transferable to any material and to a broad range of experimental testing frameworks where observations are limited and acquisition costs are high.

References:

• Plans d'expériences d'essais optimaux, 2025
• Uncertainty quantification of the reference temperature T0 of 16MND5 steel from experimental and numerical fracture toughness tests, 2025

Joint work with Jean Marc Bourinet & Cécile Mattrand (SIGMA Clermont) & Rudy Chocat (CEA Saclay) & Tom Petit (CEA Gramat)

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #96

The ninety-sixth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, March 12, 2026.

2–3 PM — Richard Everitt (Department of Statistics, University of Warwick)

Improved MCMC with active subspaces

Constantine et al. (2016) introduced a Metropolis-Hastings (MH) approach that target the active subspace of a posterior distribution: a linearly projected subspace that is informed by the likelihood.. Schuster et al. (2017) refined this approach to introduce a pseudo-marginal Metropolis-Hastings, integrating out inactive variables through estimating a marginal likelihood at every MH iteration. In this talk we show empirically that the effectiveness of these approaches is limited in the case where the linearity assumption is violated, and suggest a particle marginal Metropolis-Hastings algorithm as an alternative for this situation. The high computational cost of these approaches leads us to consider alternative approaches to using active subspaces in MCMC that avoid the need to estimate a marginal likelihood: we introduce Metropolis-within-Gibbs and Metropolis-within-particle Gibbs methods that provide a more computationally efficient use of the active subspace.

References:

• Improved MCMC with active subspaces, 2025

Joint work with Leonardo Ripoli (University of Reading)

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #95

The ninety-fifth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, February 12, 2026.

2–3 PM — Yuansi Chen (ETH Zürich) — [slides]

When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?

We analyze the mixing time of Metropolized Hamiltonian Monte Carlo (HMC) with the leapfrog integrator to sample from a distribution on $\mathbb{R}^d$ whose log-density is smooth, has Lipschitz Hessian in Frobenius norm and satisfies isoperimetry. We bound the gradient complexity to reach $\epsilon$ error in total variation distance from a warm start by $O(d^{1/4} \polylog(1/\epsilon))$ and compare it to the minimax mixing rate of MALA. We discuss the benefit of the leapfrog integrator in HMC with short integration time.

References:

• Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling, 2021
• When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?, 2023

Joint work with Khashayar Gatmiry (MIT) & Minhui Jiang (ETH Zürich)

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #94

The ninety-fourth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 22 → February 05 (rescheduled), 2026.

2–3 PM — Eleni Chatzi (ETH Zürich, Department of Civil, Environmental and Geomatic Engineering) — [slides]

Dynamics, Inference, and Uncertainty: Foundations of AI-Enhanced Digital Twins

This talk examines the role of structural dynamics as a foundation for inference under uncertainty in AI-enhanced Digital Twins. Structural assets are highly individual, operate under variable environmental and operational conditions, and are only partially observable. In this context, dynamical signatures, extracted through structured inference schemes such as modal analysis, provide compact and physically interpretable representations through which uncertainty can be quantified, propagated, and reduced.

The talk discusses how physics-enhanced machine learning (PEML), together with structured representations and reduced-order models, enables potent yet efficient approximations that synergize with available data. By embedding physical constraints, governing equations, and dynamical structure into learning architectures, these models balance prior knowledge with data-driven adaptation, reducing epistemic uncertainty while remaining scalable under limited or evolving observations. Structured low-dimensional representations further support stable learning, efficient uncertainty propagation, and interpretable model updates.

By framing dynamics as the interface between physics and data within the context of inference, the talk highlights pathways toward uncertainty-aware, interpretable digital twins capable of supporting resilient decision-making of complex infrastructure systems.

References:

• Discussing the spectrum of physics-enhanced machine learning: a survey on structural mechanics applications, 2024 - github
• On the Consistent Classification and Treatment of Uncertainties in Structural Health Monitoring Applications, 2024
• Grammar-based Ordinary Differential Equation Discovery, 2025 - github
• Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics, 2025 - github

Joint work with the further members of the group of Structural Mechanics & Monitoring at ETH Zürich

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #93

The ninety-third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 8, 2026.

2–3 PM — Masha Naslidnyk (Department of Statistical Science, University College London) — [slides]

Kernel Quantile Embeddings and Associated Probability Metrics

Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful non-parametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings (KMEs) to represent distributions as mean functions in RKHS. However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs), along with a consistent estimator. We then use KQEs to construct a family of distances that: (i) are probability metrics under weaker kernel conditions than MMD; (ii) recover a kernelised form of the sliced Wasserstein distance; and (iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations. Our findings demonstrate the value of representing distributions in Hilbert space beyond simple mean functions, paving the way for new avenues of research.

References:

• Kernel Quantile Embeddings and Associated Probability Metrics, ICML 2025

Joint work with Siu Lun Chau (NTU, Singapore) & François-Xavier Briol (UCL) & Krikamol Muandet (CISPA Helmholtz Center for Information Security).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #92

The ninety-second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 18, 2025.

2–3 PM — Lea Friedli (Engineering Risk Analysis Group, Technical University of Munich)

CRPS-Based Targeted Sequential Design with Application in Chemical Space

Gaussian processes (GPs) have become a widely used tool for modeling unknown functions across various domains. In many applications, particular interest lies in a specific range of the response, with the goal of identifying inputs that lead to desired outputs. To enhance GP model performance in this setting, we employ weighted scoring rules to develop sequential design strategies that selectively augment the training dataset. Specifically, we study pointwise and integral criteria based on the threshold-weighted Continuous Ranked Probability Score (CRPS), using two different weighting measures. We showcase an application in synthetic chemistry, where the objective is to identify molecules with specific properties. However, the presented acquisition strategies are applicable to a wide range of fields and pave the way to further developing sequential design relying on scoring rules.

References:

• CRPS-Based Targeted Sequential Design with Application in Chemical Space, 2025 - github

Joint work with Athénaïs Gautier (ONERA) & Anna Broccard (OFJ) & David Ginsbourger (IMSV, University of Bern).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

UQSay #91

The ninety first UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 4, 2025.

2–3 PM — Iain Henderson (ISAE-SUPAERO) — [slides]

Multidimensional conformal prediction with random ellipsoids

Conformal prediction (CP) is a popular framework for performing uncertainty quantification on a given a statistical predictor. Its main perks are as follow : (i) little to no assumption on the distribution of the data is required, and (ii) CP provides finite sample coverage garanties. The CP confidence regions are built using a so-called ''conformity score'', which dictates the properties of the said regions. In this talk, I will describe two new conformity scores in a general multivariate regression framework. They are based on a covariance analysis of the residuals and the input points. I will provide theoretical guarantees on the prediction sets, which consist in explicit ellipsoids. We study the asymptotic properties of the ellipsoids, and show that their volume is reduced compared to that of classic balls, under ellipticity assumptions. I will provide numerical illustrations of our results, including heavy-tailed as well as non-elliptical distributions.

References:

• Adaptive inference with random ellipsoids through Conformal Conditional Linear Expectation, 2024

Joint work with Adrien Mazoyer & Fabrice Gamboa (Institut de Mathématiques de Toulouse).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.